I have pretty ****ty street tires (Good Year Eagles that about had it at this point) ... my car is a M6.
I rev it up high enough she wont stall (around 2200ish) and feather out the clutch. By feather, I release it hard til it hooks, lay into the throttle and ease it out the rest of the way (this takes literally less than half a second). Half the time she will hook at a low enough RPM that it won't break the tires loose and I can somewhat control the wheel spin through 1st, into 2nd.
Sticky tires, well, I've found it easier to light them up, and hold the throttle at one spot exactly. When the RPM's start to drop, the tires are warming up and getting sticky enough. Stop. Stage. Rev it to incrementally higher RPM's dumping the clutch the same every time. You'll find the sweet spot where it launches good.
Also, when I let the clutch out on a launch, prior to actually launching - I let the clutch out to that point where you can "feel" it but it isn't moving the car yet (if that makes sense). This takes the drivetrain slack out of the equation somewhat and makes it easier on the entire driveline.
This is about all the advice I can offer after 15 years of launching dirt bikes, quads, cars, trucks, etc. And I don't think I ever broke on a launch yet ...
95' Z28 Vert M6, Pacesetter LT's, ORY, 3" Cutout, FM Cat-back, CAI, 1.6PM's, 918's, 10* Stuff, BRE Cam, PCMforless, 30# SVO, 255LPH Racetronix w/Hot Wire Kit, Mallory 685, 160*, LT4 KM, !AIR, !CAGS, Pro-5.0, Perma-Cool Oil Cooler, LCA, SFC, STB, PHR, TA & Cross Member, G-Load Brace.